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Solve the following equation: \(\frac{2}{(2r - 1)}\) - \(\frac{5}{3}\) =  \(\frac{1}{(r + 2)}\)

JAMB 2021

Solve the following equation: \(\frac{2}{(2r - 1)}\) - \(\frac{5}{3}\) =  \(\frac{1}{(r + 2)}\)

  • A. ( -1,\(\frac{5}{2}\) )
  • B. ( 1, - \(\frac{5}{2}\) )
  • C. ( \(\frac{5}{2}\), 1 )
  • D. (2,1)
Correct Answer: Option B
Explanation

\(\frac{2}{(2r - 1)}\) - \(\frac{5}{3}\) =  \(\frac{1}{(r + 2)}\)

\(\frac{2}{(2r - 1)}\) - \(\frac{1}{(r + 2)}\)  = \(\frac{5}{3}\)

The L.C.M.: (2r - 1) (r + 2) 

\(\frac{2(r + 2) - 1(2r - 1)}{(2r - 1) (r + 2)}\) = \(\frac{5}{3}\)

\(\frac{2r + 4 - 2r + 1}{ (2r - 1) (r + 2)}\) = \(\frac{5}{3}\)

cross multiply the solution

3 = (2r - 1) (r + 2) or 2r\(^2\) + 3r - 2 (when expanded)

collect like terms

2r\(^2\) + 3r - 2 - 3 = 0

2r\(^2\) + 3r - 5 = 0

Factorize to get x = 1 or - \(\frac{5}{2}\)

There is an explanation video available below.


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Explanation Video

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